In this talk, we revisit how partially separable structure can be exploited to improve quasi-Newton methods in large-scale continuous optimization. The partially-separable structure as a sum of element functions can be automatically deduced from the expression graph of the objective function. Partitioned quasi-Newton methods approximate the Hessian of individual element functions, and preserve the assembled Hessian sparsity. Our method is matrix- and factorization free, and allows to combine several element functions together. By updating several element functions at each iterate, we obtain a finer approximation than with unstructured quasi-Newton updates. Our numerical results illustrate the fast convergence induced by high rank updates.